$ \hat p_1 - \hat p_2 < \frac{\hat p_1 - \hat p_2}{\sqrt{\hat p(1 - \hat p)\Big(\frac{1}{n_1}+\frac{1}{n_2} \Big)}} $ where $\hat p = \frac {p_1 n_1 + p_2 n_2} {n_1 + n_2}$ In [[R]] use `prop.test(x=c(p1, p2), n=c(n1, n2))`.